Here's a problem I seen somewhere I thought was kind of fun:
Show that the arc length of sin(x) over the interval is equal to the circumference of the ellipse ".
The arc length integrals are not easily done by elementary means. At least, I don't think so
Very good curvature. That's how I tackled it. Also, the same way it was done on another forum. That is apparently the best way. I will admit, I scratched my head for a little while before it dawned on me to use parametric arc length. Then , it was obvious. Fell right into place
I get the feeling you may think I actually didn't solve the problem, but said I did it that way. Sorry, if it looks that way but I would'nt be that dishonest.
I was thinking maybe someone would show another way besides the parametric arc length method. I won't post anymore problems that way.